Aaaargh!!! I must be thinking of something else. Please disregard the above. I had a brain fart. I had it confused with "Why Don't You Do Right?" which sounds similar."Gee Baby Ain't I Good To You" was written by Andy Razaff ( Fats Waller's songwriting partner), and could probably be found on a good Fats Waller anthology.
Sorry for any inconvenience caused by the previous erroneous post.
Razaff is the author, and Waller the songs first performer.